Winning Our Future tells CNN they'll be up on Florida television "very soon" with spots supporting the former House speaker, and say they'll be "very competitive" with the super PAC that's supporting former Massachusetts Gov. Mitt Romney, who has a much larger war chest than Gingrich.Follow the Ticker on Twitter: @politicalticker

Romney's campaign has spent $2.4 million in Florida so far this cycle (through last Thursday), according to estimates by Campaign Media Analysis Group (CMAG), a company that tracks and estimates the costs of campaign ads running on the air. And Restore Our Future, an independent pro-Romney super PAC, has dished out around the same amount of money to run commercials in the Sunshine State. Through last Thursday, neither the Gingrich campaign or Restore Our Future has spent any money to air ads, according to CMAG estimates.

Gingrich topped Romney and former Sen. Rick Santorum of Pennsylvania and Rep. Ron Paul of Texas by double digits in Saturday's South Carolina GOP presidential primary, even though his campaign and the super PAC were outspent in the Palmetto State by the Romney campaign and super PAC.

But it may be a different story in Florida, which is a much more expensive state to air ads, thanks to its numerous and expensive television markets.

Winning Our Future is being bankrolled, in part, by billionaire casino mogul Sheldon Adelson, who earlier this month donated $5 million to the super PAC.